SQUID-Based Kerr Cat Qubit: Theory and Lifetime Analysis*

Kerr cat qubits are bosonic qubits encoded in a parametrically driven superconducting nonlinear oscillator. They have been studied widely using driven SNAIL transmon. We investigate an alternate design for the Kerr cat qubit, namely flux driven SQUIDs. We perform the circuit analysis and derive the Lindblad master equation for the Kerr cat qubit attached to a thermal environment. We find that the SQUID-based Kerr cat qubits have lifetimes comparable to that of SNAIL-based Kerr cat qubits for intermediate cat sizes. The SQUID-based Kerr cat qubits also have the additional benefit of being resistant against higher order photon dissipation effects. We also examine the effect of strong flux driving and asymmetric Josephson junctions on the lifetime of the qubit.